An assembly is provided for a turbine engine with a flowpath. This turbine engine assembly includes a fuel injection system. The fuel injection system includes a first fuel injector and a second fuel injector. The fuel injection system is configured to provide the first fuel injector with first fuel and provide the second fuel injector with second fuel. The first fuel may be or include ammonia. The second fuel is different than the first fuel. The second fuel may be or include hydrogen gas. The first fuel injector is configured to direct the first fuel into the flowpath for combustion. The second fuel injector is configured to direct the second fuel into the flowpath for combustion.